jmc

By simplifying exponents, we have $2^{2n}=4^n$. So, our overall expression is $\frac{4^n}{4^{n+1}}$. This simplifies to $\boxed{\frac{1}{4}}$. Throughout the course of this calculation, we did not have to plug in the value of 11 for $n$, but the answer may be similarly obtained with this substitution.